# Extensions

**Concrete** supports native Python and NumPy operations as much as possible, but not everything in Python or NumPy is available. Therefore, we provide some extensions ourselves to improve your experience.

## fhe.univariate(function)

Allows you to wrap any univariate function into a single table lookup:

```python
import numpy as np
from concrete import fhe

def complex_univariate_function(x):

    def per_element(element):
        result = 0
        for i in range(element):
            result += i
        return result

    return np.vectorize(per_element)(x)

@fhe.compiler({"x": "encrypted"})
def f(x):
    return fhe.univariate(complex_univariate_function)(x)

inputset = [np.random.randint(0, 5, size=(3, 2)) for _ in range(10)]
circuit = f.compile(inputset)

sample = np.array([
    [0, 4],
    [2, 1],
    [3, 0],
])
assert np.array_equal(circuit.encrypt_run_decrypt(sample), complex_univariate_function(sample))
```

{% hint style="danger" %}
The wrapped function:
- shouldn't have any side effects (e.g., no modification of global state)
- should be deterministic (e.g., no random numbers)
- should have the same output shape as its input (i.e., `output.shape` should be the same with `input.shape`)
- each output element should correspond to a single input element (e.g., `output[0]` should only depend on `input[0]`)

If any of these constraints are violated, the outcome is undefined.
{% endhint %}

## fhe.multivariate(function)

Allows you to wrap any multivariate function into a table lookup:

```python
import numpy as np
from concrete import fhe

def value_if_condition_else_zero(value, condition):
    return value if condition else np.zeros_like(value, dtype=np.int64)

def function(x, y):
    return fhe.multivariate(value_if_condition_else_zero)(x, y)

inputset = [
    (
        np.random.randint(-2**4, 2**4, size=(2, 2)),
        np.random.randint(0, 2**1, size=()),
    )
    for _ in range(100)
]

compiler = fhe.Compiler(function, {"x": "encrypted", "y": "encrypted"})
circuit = compiler.compile(inputset)

sample = [np.array([[-2, 4], [0, 1]]), 0]
assert np.array_equal(circuit.encrypt_run_decrypt(*sample), function(*sample))

sample = [np.array([[3, -1], [2, 4]]), 1]
assert np.array_equal(circuit.encrypt_run_decrypt(*sample), function(*sample))
```

{% hint style="danger" %}
The wrapped function:
- shouldn't have any side effects (e.g., no modification of global state)
- should be deterministic (e.g., no random numbers)
- should have input shapes which are broadcastable to the output shape (i.e., `input.shape` should be broadcastable to `output.shape` for all inputs)
- each output element should correspond to a single input element (e.g., `output[0]` should only depend on `input[0]` of all inputs)

If any of these constraints are violated, the outcome is undefined.
{% endhint %}

{% hint style="warning" %}
Multivariate functions cannot be called with [rounded](./rounding.md) inputs.
{% endhint %}

## fhe.conv(...)

Allows you to perform a convolution operation, with the same semantic as [onnx.Conv](https://github.com/onnx/onnx/blob/main/docs/Operators.md#conv):

```python
import numpy as np
from concrete import fhe

weight = np.array([[2, 1], [3, 2]]).reshape(1, 1, 2, 2)

@fhe.compiler({"x": "encrypted"})
def f(x):
    return fhe.conv(x, weight, strides=(2, 2), dilations=(1, 1), group=1)

inputset = [np.random.randint(0, 4, size=(1, 1, 4, 4)) for _ in range(10)]
circuit = f.compile(inputset)

sample = np.array(
    [
        [3, 2, 1, 0],
        [3, 2, 1, 0],
        [3, 2, 1, 0],
        [3, 2, 1, 0],
    ]
).reshape(1, 1, 4, 4)
assert np.array_equal(circuit.encrypt_run_decrypt(sample), f(sample))
```

{% hint style="danger" %}
Only 2D convolutions without padding and with one group are currently supported.
{% endhint %}

## fhe.maxpool(...)

Allows you to perform a maxpool operation, with the same semantic as [onnx.MaxPool](https://github.com/onnx/onnx/blob/main/docs/Operators.md#maxpool):

```python
import numpy as np
from concrete import fhe

@fhe.compiler({"x": "encrypted"})
def f(x):
    return fhe.maxpool(x, kernel_shape=(2, 2), strides=(2, 2), dilations=(1, 1))

inputset = [np.random.randint(0, 4, size=(1, 1, 4, 4)) for _ in range(10)]
circuit = f.compile(inputset)

sample = np.array(
    [
        [3, 2, 1, 0],
        [3, 2, 1, 0],
        [3, 2, 1, 0],
        [3, 2, 1, 0],
    ]
).reshape(1, 1, 4, 4)
assert np.array_equal(circuit.encrypt_run_decrypt(sample), f(sample))
```

{% hint style="danger" %}
Only 2D maxpooling without padding and up to 15-bits is currently supported.
{% endhint %}

## fhe.array(...)

Allows you to create encrypted arrays:

```python
import numpy as np
from concrete import fhe

@fhe.compiler({"x": "encrypted", "y": "encrypted"})
def f(x, y):
    return fhe.array([x, y])

inputset = [(3, 2), (7, 0), (0, 7), (4, 2)]
circuit = f.compile(inputset)

sample = (3, 4)
assert np.array_equal(circuit.encrypt_run_decrypt(*sample), f(*sample))
```

{% hint style="danger" %}
Currently, only scalars can be used to create arrays.
{% endhint %}

## fhe.zero()

Allows you to create an encrypted scalar zero:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x):
    z = fhe.zero()
    return x + z

inputset = range(10)
circuit = f.compile(inputset)

for x in range(10):
    assert circuit.encrypt_run_decrypt(x) == x
```

## fhe.zeros(shape)

Allows you to create an encrypted tensor of zeros:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x):
    z = fhe.zeros((2, 3))
    return x + z

inputset = range(10)
circuit = f.compile(inputset)

for x in range(10):
    assert np.array_equal(circuit.encrypt_run_decrypt(x), np.array([[x, x, x], [x, x, x]]))
```

## fhe.one()

Allows you to create an encrypted scalar one:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x):
    z = fhe.one()
    return x + z

inputset = range(10)
circuit = f.compile(inputset)

for x in range(10):
    assert circuit.encrypt_run_decrypt(x) == x + 1
```

## fhe.ones(shape)

Allows you to create an encrypted tensor of ones:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x):
    z = fhe.ones((2, 3))
    return x + z

inputset = range(10)
circuit = f.compile(inputset)

for x in range(10):
    assert np.array_equal(circuit.encrypt_run_decrypt(x), np.array([[x, x, x], [x, x, x]]) + 1)
```

## fhe.hint(value, **kwargs)

Allows you to hint properties of a value. Imagine you have this circuit:

```python
from concrete import fhe
import numpy as np

@fhe.compiler({"x": "encrypted"})
def f(x, y, z):
    a = x | y
    b = y & z
    c = a ^ b
    return c

inputset = [
    (np.random.randint(0, 2**8), np.random.randint(0, 2**8), np.random.randint(0, 2**8))
    for _ in range(3)
]
circuit = f.compile(inputset)

print(circuit)
```

You'd expect all of `a`, `b`, and `c` to be 8-bits, but because inputset is very small, this code could print:

```
%0 = x                          # EncryptedScalar<uint8>        ∈ [173, 240]
%1 = y                          # EncryptedScalar<uint8>        ∈ [52, 219]
%2 = z                          # EncryptedScalar<uint8>        ∈ [36, 252]
%3 = bitwise_or(%0, %1)         # EncryptedScalar<uint8>        ∈ [243, 255]
%4 = bitwise_and(%1, %2)        # EncryptedScalar<uint7>        ∈ [0, 112] 
                                                  ^^^^^ this can lead to bugs
%5 = bitwise_xor(%3, %4)        # EncryptedScalar<uint8>        ∈ [131, 255]
return %5
```

The first solution in these cases should be to use a bigger inputset, but it can still be tricky to solve with the inputset. That's where `hint` extension comes into play. Hints are a way to provide extra information to compilation process:

- Bit-width hints are for constraining the minimum number of bits in the encoded the value. If you hint a value to be 8-bits, it means it should be at least `uint8` or `int8`.

To fix `f` using hints, you can do:

```python
@fhe.compiler({"x": "encrypted", "y": "encrypted", "z": "encrypted"})
def f(x, y, z):
    # hint that inputs should be considered at least 8-bits
    x = fhe.hint(x, bit_width=8)
    y = fhe.hint(y, bit_width=8)
    z = fhe.hint(z, bit_width=8)

    # hint that intermediates should be considered at least 8-bits
    a = fhe.hint(x | y, bit_width=8)
    b = fhe.hint(y & z, bit_width=8)
    c = fhe.hint(a ^ b, bit_width=8)

    return c
```

{% hint style="warning" %}
Hints are only applied to the value being hinted, and no other value. If you want the hint to be applied to multiple values, you need to hint all of them.
{% endhint %}

you'll always see:

```
%0 = x                          # EncryptedScalar<uint8>        ∈ [...]
%1 = y                          # EncryptedScalar<uint8>        ∈ [...]
%2 = z                          # EncryptedScalar<uint8>        ∈ [...]
%3 = bitwise_or(%0, %1)         # EncryptedScalar<uint8>        ∈ [...]
%4 = bitwise_and(%1, %2)        # EncryptedScalar<uint8>        ∈ [...] 
%5 = bitwise_xor(%3, %4)        # EncryptedScalar<uint8>        ∈ [...]
return %5
```

regardless of the bounds.

Alternatively, you can use it to make sure a value can store certain integers:

```python
@fhe.compiler({"x": "encrypted", "y": "encrypted"})
def is_vectors_same(x, y):
    assert x.ndim != 1
    assert y.ndim != 1
    
    assert len(x) == len(y)
    n = len(x)
    
    number_of_same_elements = np.sum(x == y)
    fhe.hint(number_of_same_elements, can_store=n)  # hint that number of same elements can go up to n
    is_same = number_of_same_elements == n

    return is_same
```
